Submerged periodic riblets

ABSTRACT

In one embodiment, a method for reducing drag includes forming a smooth surface on a first portion of a physical object. The method also includes forming periodic riblets on a second portion of the physical object. The second portion of the physical object is adjacent to the first portion of the physical object. Each riblet of the periodic riblets of the second portion of the physical object is depressed below a plane of the smooth surface of the first portion of the physical object. The method further includes generating a flow over the periodic riblets of the second portion of the physical object and over the smooth surface of the first portion of the physical object. A length of each riblet of the periodic riblets runs parallel to a direction of the flow.

TECHNICAL FIELD

This disclosure generally relates to riblets, and more specifically tosubmerged periodic riblets.

BACKGROUND

An object (e.g., an aircraft or a marine vessel) that moves through afluid (e.g., air or water) experiences a drag force. An increase in thedrag force experienced by the object increases the energy required forthe object to move through the fluid. For example, an increase in thedrag force experienced by an aircraft moving at an established speed mayincrease the power required by the aircraft to move through the air atthe same established speed. Thus, drag force has a significant impact ofaircraft fuel consumption and aircraft range.

SUMMARY

According to an embodiment, a method for reducing drag includes forminga smooth surface on a first portion of a physical object. The methodalso includes forming periodic riblets on a second portion of thephysical object. The second portion of the physical object is adjacentto the first portion of the physical object. Each riblet of the periodicriblets of the second portion of the physical object is depressed belowa plane of the smooth surface of the first portion of the physicalobject. The method further includes generating a flow over the periodicriblets of the second portion of the physical object and over the smoothsurface of the first portion of the physical object. A length of eachriblet of the periodic riblets runs parallel to a direction of the flow.

According to another embodiment, a physical object includes a firstportion having a smooth surface. The physical object further includes asecond portion having periodic riblets. The second portion of thephysical object is adjacent to the first portion of the physical object.Each riblet of the periodic riblets of the second portion of thephysical object is depressed below a plane of the smooth surface of thefirst portion of the physical object.

According to yet to another embodiment, a method of manufacturing aphysical object includes forming a smooth surface on a first portion ofa physical object. The method further includes forming periodic ribletson a second portion of the physical object. The second portion of thephysical object is adjacent to the first portion of the physical object.Each riblet of the periodic riblets of the second portion of thephysical object is depressed below a plane of the smooth surface of thefirst portion of the physical object.

Technical advantages of this disclosure may include one or more of thefollowing. The use of submerged ribbed surfaces on physical objectsreduces overall drag (which includes pressure and viscous drag)experienced by the physical object as compared to physical objectshaving a smooth surface, which may significantly reduce fuel costs sinceless power is required to move the object through the fluid (e.g., gasor liquid). The drag reduction experienced by a physical object such asan aircraft that uses submerged ribbed surfaces may also increase therange (i.e., the maximum distance the aircraft can fly between takeoffand landing) of the physical object as compared to physical objects thathave a smooth surface. In certain embodiments, the drag reduction mayallow higher maximum speeds to be obtained for a fixed propulsion input.In some embodiments, submerged periodic riblets may reduce heat transferon a hot or cold surface adjacent to a turbulent boundary layer, whichmay reduce the insulation required in particular applications. The useof submerged periodic riblets may delay or prevent the separation of theflow in a turbulent boundary layer from the surface, which may reduceaerodynamic drag, increase lift on a physical object (e.g., an aircraftwing), and/or improve the performance of propulsion systems.

Other technical advantages will be readily apparent to one skilled inthe art from the following figures, descriptions, and claims. Moreover,while specific advantages have been enumerated above, variousembodiments may include all, some, or none of the enumerated advantages.

BRIEF DESCRIPTION OF THE DRAWINGS

To assist in understanding the present disclosure, reference is now madeto the following description taken in conjunction with the accompanyingdrawings, in which:

FIG. 1A illustrates a physical object with submerged periodic riblets,in accordance with an example embodiment;

FIG. 1B illustrates a longitudinal section of the physical object ofFIG. 1A, in accordance with an example embodiment;

FIG. 2A illustrates a cross section of a protruding riblet pattern, inaccordance with an example embodiment;

FIG. 2B illustrates a cross section of a submerged riblet pattern, inaccordance with an example embodiment;

FIG. 3A illustrates a pressure output pattern associated with a physicalobject having a protruding riblet pattern, in accordance with an exampleembodiment;

FIG. 3B illustrates a pressure output pattern associated with a physicalobject having a submerged riblet pattern, in accordance with an exampleembodiment;

FIG. 4 illustrates a bar chart that compares drag produced by a physicalobject having a protruding riblet pattern to a physical object having asubmerged riblet pattern, in accordance with an example embodiment; and

FIG. 5 illustrates an example method for reducing drag on a surfaceusing a submerged riblet pattern, in accordance with an exampleembodiment.

DETAILED DESCRIPTION

Embodiments of this disclosure describe physical objects havingsubmerged periodic riblets that may be used to reduce total drag, whichincludes pressure drag and friction drag, over the surfaces of thephysical objects. Riblets are very small (e.g., less than a hundredth ofan inch in depth) grooves or channels on a surface of a physical object(e.g., a vehicle). The riblets run parallel to the direction of flow.Submerged periodic riblets are regions with riblets that are submergedbelow a smooth surface of the physical object. The regions havingsubmerged periodic riblets may be followed by a short section of asmooth surface. This intermittent pattern may be repeated for the lengthof the surface of the physical object.

While conventional riblets that protrude above the surface of thephysical object reduce drag by suppressing near wall turbulentstructures, conventional riblets also increase the wetted area. Theconcept of the submerged periodic riblets disclosed herein relies on thefact that that the damping of turbulent structures persists beyond theend of the riblet section, which reduces drag over the riblet and smoothregions. Alternating the smooth and riblet regions reduces drag byreducing the wetted area. Submerging the riblets reduces pressure dragin the transition regions between the smooth surface and the ribletsurface as compared to protruding periodic or variable height riblets.As such, embodiments of this disclosure use submerged periodic ribletsto reduce the pressure drag penalty of the periodic riblet conceptrelative to the protruding periodic riblets.

FIGS. 1 through 5 show example apparatuses and methods associated withsubmerged periodic riblets. FIG. 1A shows an example physical objectwith submerged periodic riblets and FIG. 1B shows an examplelongitudinal section of the physical object of FIG. 1A. FIG. 2A shows anexample cross section of a protruding riblet pattern and FIG. 2B showsan example cross section of a submerged riblet pattern. FIG. 3A shows anexample pressure output pattern associated with a physical object havinga protruding riblet pattern and FIG. 3B shows an example pressure outputpattern associated with a physical object having a submerged ribletpattern. FIG. 4 shows an example bar chart that compares drag producedby a physical object having a protruding riblet pattern to a physicalobject having a submerged riblet pattern. FIG. 5 shows an example methodfor reducing drag on a surface using a submerged riblet pattern.

FIG. 1A illustrates an example physical object 100 having submergedperiodic riblets 110. Physical object 100 with submerged periodicriblets 110 may be used to reduce overall drag (e.g., aerodynamic orhydrodynamic drag) over a surface as compared to physical object 100without submerged periodic riblets 110 or physical object 100 withprotruding periodic riblets (e.g., protruding riblets 212 of FIG. 2A.)One or more portions of physical object 100 may be made of steel,aluminum, copper, titanium, nickel, plastic, fiberglass, a combinationthereof, or any other suitable material.

Physical object 100 is any object that is susceptible to drag (e.g.,skin friction drag and pressure drag.) For example, physical object 100may be a component (e.g., a portion of an outer body) of an aircraft(e.g., an airplane, a helicopter, a blimp, a drone, etc.), a componentof a marine vessel (e.g., a cargo ship, a passenger ship, a canoe, araft, etc.), a component of a motorized vehicle (e.g., a truck, a car, atrain, a scooter, etc.), a component of a non-motorized vehicle (e.g., abicycle, a skateboard, etc.), a component of a spacecraft (e.g., aspaceship, a satellite, etc.), a wind turbine, a projectile (e.g., amissile), or any other physical object that is capable of experiencingdrag. In certain embodiments, drag is generated by a force actingopposite to the relative motion of physical object 100 (e.g., a wing ofan aircraft) moving with respect to a surrounding fluid (e.g., air). Insome embodiments, drag is generated by the viscosity of gas. In certainembodiments, drag is generated due to the viscosity of a fluid (e.g.,water) near the surface of physical object 100 (e.g., a section of apipe or duct.)

Physical object 100 of FIG. 1A includes a first portion 120, a secondportion 130, and a third portion 140. First portion 120 has a smoothsurface 130, second portion 130 has a ribbed surface 132, and thirdportion 140 has a smooth surface 142. In certain embodiments, smoothsurface 122 of first portion 120 and/or smooth surface 142 of thirdportion 140 is flat. In some embodiments, smooth surface 122 of firstportion 120 and/or smooth surface 142 of third portion 140 may have acurvature. In the illustrated embodiment of FIG. 1A, smooth surface 122of first portion 120 of physical object 100 is along a same plane (e.g.,plane 180 of FIG. 1B) as smooth surface 142 of third portion 140 ofphysical object 100. Second portion 120 of physical object 100 includessubmerged periodic riblets 110. Submerged periodic riblets 110 of secondportion 130 form ribbed surface 132.

Submerged periodic riblets 110 of second portion 130 of physical object100 span from first portion 120 of physical object 100 to third portion140 of physical object 100. Each submerged periodic riblet 110 ofphysical object 100 is depressed below a plane of smooth surface 122 offirst portion 120 such that no portion of submerged periodic riblet 110extends beyond the plane of smooth surface 122 of first portion 120 in adirection away from physical object 100.

Each submerged periodic riblet 110 includes a peak 112. Each peak 112 ofeach submerged periodic riblet 110 is a location (e.g., a point, aplane, a ridge, etc.) along an exterior surface of submerged periodicriblet 110 that is closest to the plane of smooth surface 122. In theillustrated embodiment of FIG. 1A, peaks 112 of submerged periodicriblets 110 reach the plane of smooth surface 122 of physical object100. In some embodiments, one or more peaks 112 of one or more submergedperiodic riblets 110 may form a pointed tip. In some embodiments, one ormore peaks 112 of one or more submerged periodic riblets 110 may form aflat or rounded peak surface.

The intersections of adjacent submerged periodic riblets 110 createvalleys 114. Each valley 114 between adjacent submerged periodic riblets110 is a location along an exterior surface of submerged periodic riblet110 that is farthest away from the plane of smooth surface 122. In theillustrated embodiment of FIG. 1A, valleys 114 of submerged periodicriblets 110 are located below the plane of smooth surface 122 ofphysical object 100. In some embodiments, submerged periodic riblets 110may be spaced apart such that adjacent submerged periodic riblets 110 donot intersect. For example, each valley 114 between each submergedperiodic riblet 110 may be a flat or rounded valley surface. In certainembodiments, one or more valleys 114 of one or more submerged periodicriblets 110 may form a pointed tip.

Although physical object 100 of FIG. 1A illustrates a particular numberof submerged periodic riblets 110, peaks 112, valleys 114, firstportions 120, smooth surfaces 122, second portions 130, ribbed surfaces132, third portions 140, and smooth surfaces 142, this disclosurecontemplates any suitable number of submerged periodic riblets 110,peaks 112, valleys 114, first portions 120, smooth surfaces 122, secondportions 130, ribbed surfaces 132, third portions 140, and smoothsurfaces 142. For example, physical object 100 of FIG. 1A may include afourth portion with a submerged ribbed surface adjacent to third portion140 having smooth surface 142.

Although physical object 100 of FIG. 1A illustrates a particulararrangement of submerged periodic riblets 110, peaks 112, valleys 114,first portion 120, smooth surface 122, second portion 130, ribbedsurface 132, third portion 140, and smooth surface 142, this disclosurecontemplates any suitable arrangement of submerged periodic riblets 110,peaks 112, valleys 114, first portion 120, smooth surface 122, secondportion 130, ribbed surface 132, third portion 140, and smooth surface142. For example, smooth surface 142 of third portion 140 may be at adifferent plane than smooth surface 122 of first portion 120. As anotherexample, peaks 112 of submerged periodic riblets 110 may be recessedbelow the plane of smooth surface 122 of first portion 120.

FIG. 1B illustrates an example longitudinal section 150 of physicalobject 100 of FIG. 1A. Longitudinal section 150 of FIG. 1B is cutthrough surface 122 of first portion 120, valley 114 of second portion130, and smooth surface 142 of third portion 140. First portion 120 ofphysical object 100 has a length L1, second portion 120 of physicalobject 100 has a length L2, and third portion 140 of physical object 100has a length L3. In the illustrated embodiment of FIG. 1B, eachsubmerged periodic riblet 110 of second portion 130 has approximately(within ten percent) a same length L2. In some embodiments, one or moresubmerged periodic riblets 110 of second portion 130 may have differentlengths.

In the illustrated embodiment of FIG. 1B, length L1 of first portion 120is approximately the same as length L2 of second portion 130 and lengthL3 of third portion 140 is approximately the same as length L2 of secondportion 130. While length L1, length L2, and length L3 in theillustrated embodiment of FIG. 1B are approximately the same length,length L1, length L2, and length L3 may be any suitable length. Forexample, length L1, length L2, and/or length L3 may vary by a factor oftwo.

Length L2 of submerged periodic riblets 110 of physical object 100 runsparallel to a flow direction 155. For example, physical object 100 maybe a wing of an aircraft, and length L2 of submerged periodic riblets110 of physical object 100 may run parallel to flow direction 155generated by the aircraft when the aircraft is in flight. In theillustrated embodiment of FIG. 1B, peak 112 of submerged periodic riblet110 is level with plane 180 of smooth surface 122 of physical object100.

First portion 120 of physical object 100 includes a transition surface160. An angle 170 between transition surface 160 of first portion 120 ofphysical object 100 and smooth surface 122 of first portion 120 ofphysical object 100 is within a range of 90 degrees to 179 degrees(e.g., 170 degrees.) Each submerged periodic riblet 110 terminates, in afirst direction, at transition surface 160 of first portion 120 ofphysical object 100. Third portion 140 of physical object 100 includes atransition surface 162. An angle 172 between transition surface 162 ofthird portion 140 of physical object 100 and smooth surface 142 of thirdportion 140 of physical object 100 is within a range of 90 degrees to179 degrees (e.g., 170 degrees.) Each submerged periodic riblet 110terminates, in a second direction opposite the first direction, attransition surface 162 of third portion 140 of physical object 100.

In certain embodiments, the intermittent pattern created by smoothsurface 122 of first portion 120, submerged periodic riblets 110 ofsecond portion 130, and smooth surface 142 of third portion 140 repeatsalong a predetermined length. For example, this intermittent pattern mayrepeat along the width of an airplane wing. Length L1, length L2, andlength L3 are measured from the center of transition surfaces betweeneach portion of physical object 100. For example, as illustrated in FIG.1B, length L2 is measured from the center of transition surface 160 tothe center of transition surface 162 along plane 180 of smooth surface122 of physical object 100.

FIG. 2A illustrates an example cross section 200 of a protruding ribletpattern 210. Protruding riblet pattern 210 is a pattern of protrudingriblets 212 that protrude above a plane of an adjacent surface. Forexample, referring to the illustrated embodiment of FIG. 1A, protrudingriblets 212 would be located above the plane of smooth surface 122 offirst portion 120 of physical object 100 such that each valley 216between adjacent protruding riblets 212 may be located along the planeof smooth surface 122 of first portion 120 of physical object 100. Aphysical object (e.g., physical object 100 of FIG. 1) having a ribbedsurface of protruding riblets 212 experiences less friction drag whensubjected to dynamic (e.g., aerodynamic or hydrodynamic) flow than acomparable physical object having a smooth surface. However, due to thegeometry of protruding riblet pattern 210, a physical object having aribbed surface of protruding riblets 212 experiences higher pressuredrag when subjected to dynamic flow than a comparable physical objecthaving a smooth surface.

In the illustrated embodiment of FIG. 2A, protruding riblet pattern 210protrudes above baseline 220. Baseline 220 is equivalent to a plane ofan adjacent surface (e.g., smooth surface 122 of FIG. 1A). Protrudingriblet pattern 210 of FIG. 2A is a sawtooth pattern. Each protrudingriblet 212 of protruding riblet pattern 210 has a peak 214. Peak 214 ofeach protruding riblet 212 has a height relative to baseline 220 of lessthan 0.002 inches. In certain embodiments, the height of each peak 214of each protruding riblet 212 may be within a range of 0.001 inches to0.002 inches (e.g., 0.0018 inches). Each peak 214 of each protrudingriblet 212 forms an angle 230. Angle 230 may range from 45 degrees to135 degrees. In the illustrated embodiment of FIG. 2A, angle 230 is 90degrees. In certain embodiments, each protruding riblet 212 may be atwo-dimensional (2D), thin plate riblet that is perpendicular to andlocated above baseline 220 of cross section 200. The 2D, thin plateriblets may create a series of channels with thin blades defining thechannel walls.

Adjacent protruding riblets 212 of protruding riblet pattern 210 formvalleys 216. Each valley 216 of each protruding riblet 212 is located atbaseline 220. Each valley 216 forms an angle 240. Angle 240 may rangefrom 45 degrees to 135 degrees. In the illustrated embodiment of FIG.2A, angle 240 is 90 degrees. In some embodiments, one or more valleys216 may be located above baseline 220. For example, each valley 216 ofeach protruding riblet 212 may be located 0.0002 inches above baseline220.

Each protruding riblet 212 of cross section 200 may be approximatelyequal in size, shape, and/or orientation relative to baseline 220. Inthe illustrated embodiment of FIG. 2A, each protruding riblet 212 ofprotruding riblet pattern 210 is in the shape of a triangle having twosides 242 and a base 244. Each side 242 of each protruding riblet 212has a length less than 0.004 inches. In certain embodiments, the lengthof each side 242 of each protruding riblet 212 of protruding ribletpattern 210 is within a range of 0.002 inches to 0.003 inches (e.g.,0.0025 inches). Each base 244 of each protruding riblet 212 has a lengthless than 0.005 inches. In certain embodiments, the length of each base244 of each protruding riblet 212 of protruding riblet pattern 210 iswithin a range of 0.003 inches to 0.004 inches (e.g., 0.0035 inches).

Although cross section 200 of FIG. 2A illustrates a particular number ofprotruding riblets 212, peaks 214, and valleys 216, this disclosurecontemplates any suitable number of protruding riblets 212, peaks 214,and valleys 216. For example, protruding riblet pattern 210 of FIG. 2Amay include more or less than seven protruding riblets 212. Althoughcross section 200 of FIG. 2A illustrates a particular arrangement ofprotruding riblets 212, peaks 214, and valleys 216, this disclosurecontemplates any suitable arrangement of protruding riblets 212, peaks214, and valleys 216. For example, two or more protruding riblets 212 ofFIG. 2A may have different sizes, shapes, and/or orientations relativeto baseline 220. As another example, two or more peaks 214 of two ormore protruding riblets 212 may have different heights above baseline220. As still another example, one or more peaks 214 and/or valleys 216of one or more protruding riblets 212 may be rounded or flat. As yetanother example, the length of sides 242 and base 244 may be the same toform equilateral triangles.

As illustrated in cross section 200 of FIG. 2A, the geometry of aphysical object that uses protruding riblet pattern 210 increases thewetted area as compared to a smooth surface. As such, while a physicalobject with a protruding riblet pattern 210 experiences less frictiondrag when subjected to dynamic flow than a comparable physical objecthaving a smooth surface, the pressure drag increases due to theincreased projected area in the flow direction.

FIG. 2B illustrates an example cross section 250 of a submerged ribletpattern 260. Submerged riblet pattern 260 is a pattern of repeatingsubmerged riblets that are located below a plane (e.g., plane 180 ofFIG. 1B) of an adjacent surface. For example, submerged periodic riblets262 may be equivalent to submerged periodic riblets 110 of FIG. 1A,which are located below the plane of smooth surface 122 of first portion120 of physical object 100. A physical object with a submerged ribbedsurface that uses submerged riblet pattern 260 experiences less frictiondrag when subjected to dynamic flow than a comparable physical objecthaving a smooth surface. While a physical object with a submerged ribbedsurface that uses submerged riblet pattern 260 experiences higherpressure drag when subjected to dynamic flow than a comparable physicalobject having a smooth surface, the pressure drag created by submergedriblet pattern 260 is significantly less than the pressure drag createdby protruding riblet pattern 210 of FIG. 2A.

In the illustrated embodiment of FIG. 2B, submerged riblet pattern 260is recessed below baseline 270. Baseline 270 is equivalent to a plane ofan adjacent surface (e.g., smooth surface 122 of FIG. 1A). Submergedriblet pattern 260 of FIG. 2B is a sawtooth pattern. Each submergedriblet 262 of submerged riblet pattern 250 has a peak 264. Each peak 264of each submerged riblet 262 is located at baseline 220. Each peak 264forms an angle 280. Angle 280 may range from 45 degrees to 135 degrees.In the illustrated embodiment of FIG. 2B, angle 280 is 90 degrees.

Adjacent submerged riblets 262 of submerged riblet pattern 260 formvalleys 266. Each valley 266 of each submerged riblet 262 has a depthrelative to baseline 270 of less than 0.002 inches. In certainembodiments, the depth of each valley 266 of each submerged riblet 262may be within a range of 0.001 inches to 0.002 inches (e.g., 0.0018inches). Each valley 266 of each submerged riblet 262 forms by an angle290. Angle 290 may range from 45 degrees to 135 degrees. In theillustrated embodiment of FIG. 2B, angle 290 is 90 degrees. In certainembodiments, each submerged riblet 262 may be a two-dimensional (2D),thin plate riblet that is perpendicular to and located below baseline270 of cross section 250. The 2D, thin plate riblets may create a seriesof channels with thin blades defining the channel walls.

Each submerged riblet 262 of cross section 250 may be equal in size,shape, and/or orientation. In the illustrated embodiment of FIG. 2B,each submerged riblet 262 of submerged riblet pattern 260 is in theshape of a triangle having two sides 292 and a base 294. Each side 292of each submerged riblet 262 has a length less than 0.004 inches. Incertain embodiments, the length of each side 292 of each submergedriblet 262 of submerged riblet pattern 260 is within a range of 0.002inches to 0.003 inches (e.g., 0.0025 inches). Each base 294 of eachsubmerged riblet 262 has a length less than 0.005 inches. In certainembodiments, the length of each base 294 of each submerged riblet 262 ofsubmerged riblet pattern 260 is within a range of 0.003 inches to 0.004inches (e.g., 0.0035 inches).

The sizes of submerged riblets 262 depends on the application ofsubmerged riblet pattern 260. For example, the sizes of each submergedriblets 262 may depend on the speed of fluid, the viscosity and/ordensity of the fluid, the scale of the object (e.g., physical object 100of FIG. 1), etc. In certain applications, submerged riblets 262 are lessthan a hundredth of an inch in depth. For a highly viscous fluid (e.g.,oil), submerged riblets 262 may be greater than a hundredth of an inchin depth. In certain embodiments, submerged riblets 262 may be sizedusing turbulent wall scaling. For example, submerged riblets 262 may besized according to the following formula: non-dimensional scalingh+=(height)*sqrt((density)*(wall shear stress))/(viscosity), where h+may be set to a value between 5 and 16. As another example, submergedriblets 262 may be sized according to the following formula:nondimensional spanwise spacing s+=(spanwisespacing)*sqrt((density)*(wall shear stress))/(viscosity), where s+ maybe set to a value between 8 and 25.

Although cross section 250 of FIG. 2B illustrates a particular number ofsubmerged riblets 262, peaks 264, and valleys 266, this disclosurecontemplates any suitable number of submerged riblets 262, peaks 264,and valleys 266. For example, submerged riblet pattern 260 of FIG. 2Bmay include more or less than seven submerged riblets 262. Althoughcross section 250 of FIG. 2B illustrates a particular arrangement ofsubmerged riblets 262, peaks 264, and valleys 266, this disclosurecontemplates any suitable arrangement of submerged riblets 262, peaks264, and valleys 266. For example, two or more submerged riblets 262 ofFIG. 2B may have different sizes, shapes, and/or orientations. Asanother example, two or more valleys 266 between adjacent submergedriblets 262 may have different depths below baseline 270. As stillanother example, two or more peaks 264 of two or more submerged riblets262 may be located below baseline 270. As yet another example, thelength of sides 292 and base 294 of one or more submerged riblets 262may be the same to form equilateral triangles.

FIG. 3A illustrates an example pressure pattern 300 associated with aprotruding riblet pattern 340 (e.g., protruding riblet pattern 210 ofFIG. 2A). Pressure pattern 300 was created using a simulation of a smallscale structure 310 representative of a physical object (e.g., physicalobject 100 of FIG. 1A). The simulation was performed in a low Reynoldsnumber channel with limited spanwise and streamwise extent. The effectsof the pressure gradients illustrated in FIG. 3A were assessed from ahighly resolved computational large eddy simulation of the ribletconfiguration in a channel flow. The simulation mimics the flow of afluid (e.g., a liquid or gas) on a surface having a protruding ribletpattern. The flow direction 305 is parallel to the protruding riblets ofprotruding riblet pattern 340. The output of the simulation is displayedin FIG. 3A as pressure pattern 300.

Structure 310 of pressure pattern 300 includes smooth surfaces 320similar to smooth surfaces 122 and 142 of FIG. 1A. Structure 310 ofpressure pattern 300 includes protruding ribbed surfaces 330 thatprotrude above the plane of smooth surfaces 320. Protruding ribbedsurfaces 330 form protruding riblet pattern 340. In the illustratedembodiment of FIG. 3A, protruding riblet pattern 340 is a sawtoothpattern similar to protruding riblet pattern 210 of FIG. 2A.

Pressure pattern 300 of FIG. 3A shows a distribution of time averagedpressure coefficient (Cp) as generated by the simulation. Cp is anon-dimensional parameter defined as the ratio of a difference between alocal pressure and a free stream pressure and a free stream dynamicpressure. A Cp value of zero indicates that the pressure at a particularpoint is the same as the free stream pressure, a Cp value of oneindicates a stagnation point, and a CP value less than zero indicatesthat the local velocity is greater than the free stream velocity. In theillustrated embodiment of FIG. 3A, Cp represents a time average pressuretaken over a predetermined amount of time. Cp is represented as agrayscale in the embodiment of FIG. 3A. The lowest Cp value (i.e.,−0.040) is the darkest shade in the grayscale and the highest Cp value(i.e., 0.040) is the lightest shade in the grayscale. As such, thegrayscale lightens in shade as the Cp value increases.

As indicated by the different shades of gray in pressure output pattern300 of FIG. 3A, protruding riblet pattern 340 produces a large variantof Cp values ranging from −0.040 to 0.040. The highest Cp values aregenerated in forward facing transition regions 344 between smoothsurfaces 320 and protruding riblet surfaces 330 as the flow travels inflow direction 305 from smooth surfaces 320 to protruding ribletsurfaces 330. The lowest Cp values are generated in aft facingtransition regions 346 between smooth surfaces 320 and protruding ribletsurfaces 330 as the flow travels in flow direction 305 from protrudingribbed surfaces 330 to smooth surfaces 320. The submerged riblet patternmitigates these pressure differentials by producing a more constantpressure over the surfaces of the structure, as described below in FIG.3B.

FIG. 3B illustrates an example pressure pattern 350 associated with asubmerged riblet pattern 390 (e.g., submerged riblet pattern 260 of FIG.2B). Pressure pattern 350 was created using the same simulationtechnique of FIG. 3A. Flow direction 355 is parallel to the submergedriblets of submerged riblet pattern 390. The output of the simulation isdisplayed in FIG. 3B as pressure pattern 350.

Structure 360 of pressure pattern 350 includes smooth surfaces 370similar to smooth surfaces 122 and 142 of FIG. 1A. Structure 360 ofpressure pattern 350 includes submerged ribbed surfaces 380 that arerecessed below the plane of smooth surfaces 370. Submerged ribbedsurfaces 380 form submerged riblet pattern 390. In the illustratedembodiment of FIG. 3B, submerged riblet pattern 390 is a sawtoothpattern similar to submerged riblet pattern 260 of FIG. 2B.

As indicated by the different shades of gray in pressure output pattern350 of FIG. 3B, submerged riblet pattern 390 produces a small variant ofCp values ranging from −0.016 to 0.016. Positive Cp values ofapproximately 0.008 are generated along submerged ribbed surfaces 380and negative Cp values of approximately −0.008 are generated alongsmooth surfaces 370. As such, submerged riblet pattern shown 360 in FIG.3B mitigates the pressure differentials shown in pressure pattern 300 ofFIG. 3A by producing more constant pressures over the surfaces ofstructure 360.

FIG. 4 illustrates an example bar chart 400 that compares drag producedby a physical object having a protruding riblet pattern to a physicalobject having a submerged riblet pattern. The pressure drag and viscousdrag increments are calculated from a time average of the forces in acomputational large eddy simulation of the flow in a channel withconstant cross section in the spanwise direction. Periodic boundaryconditions are applied in the spanwise direction to approximate a 2Dchannel flow of infinite span. The simulation includes a smooth surfaceon one wall of the channel and a riblet wall on the opposing channelwall. The difference in the drag components between the smooth wall andthe riblet wall provides the increments shown in FIG. 4.

Bar chart 400 includes drag differences for a protruding riblet pattern410 and a submerged riblet pattern 420. Protruding riblet pattern 410 isequivalent to protruding riblet pattern 210 of FIG. 2A. Submerged ribletpattern 410 is equivalent to submerged riblet pattern 260 of FIG. 2B.The drag for protruding riblet pattern 410 and submerged riblet pattern420 is measured as a percentage difference from the drag generated by asmooth surface without riblets. Pressure drag differences, friction(e.g., viscous) drag differences, and total drag differences areprovided in bar chart 400.

Protruding riblet pattern 410, as illustrated in bar chart 400 of FIG.4, generates a percent pressure drag difference 412 of positive sevenpercent, which indicates that protruding riblet pattern 410 generates apressure drag that is seven percent greater than the negligible pressuredrag generated by a smooth surface. Protruding riblet pattern 410generates a percent viscous drag difference 414 of negative fivepercent, which indicates that protruding riblet pattern 410 generates aviscous drag that is five percent lower than the viscous drag generatedby a smooth surface. The total drag difference, which is calculated byadding pressure drag difference 412 and viscous drag difference 414 ofprotruding riblet pattern 410, is positive two percent, which indicatesthat protruding riblet pattern 410 generates a total drag that is twopercent higher than the total drag generated by a smooth surface. Thus,while protruding riblet pattern 410 is effective at reducing viscousdrag as compared to a smooth surface without riblets, protruding ribletpattern 410 increases the overall drag when taking into considerationpressure drag.

Submerged riblet pattern 420, as illustrated in bar chart 400 of FIG. 4,generates a percent pressure drag difference 422 of positive twopercent, which indicates that submerged riblet pattern 420 generates apressure drag that is two percent greater than the pressure draggenerated by a smooth surface. Submerged riblet pattern 420 generates apercent viscous drag difference 424 of negative four percent, whichindicates that submerged riblet pattern 420 generates a viscous dragthat is four percent lower than the viscous drag generated by a smoothsurface. The total drag difference, which is calculated by addingpressure drag difference 422 and viscous drag difference 424 ofsubmerged riblet pattern 420, is negative two percent, which indicatesthat submerged riblet pattern 420 generates a total drag that is twopercent lower than the total drag generated by a smooth surface. Thus,submerged riblet pattern 420 is effective at reducing viscous drag ascompared to a smooth surface without riblets and is also effective atreducing the overall drag when taking into consideration both viscousdrag and pressure drag.

FIG. 5 illustrates an example method 500 for reducing drag on a surfacehaving a submerged riblet pattern, in accordance with an exampleembodiment. Method 500 starts at step 510. At step 520, a smooth surface(e.g., smooth surface 122 of FIG. 1A) is formed on a first portion(e.g., first portion 120 of FIG. 1A) of a physical object (e.g.,physical object 100 of FIG. 1A). The physical object may be a component(e.g., a portion of an outer body) of an aircraft (e.g., an airplane, ahelicopter, a blimp, a drone, etc.), a component of a of a marine vessel(e.g., a cargo ship, a passenger ship, a canoe, a raft, etc.), acomponent of a motorized vehicle (e.g., a truck, a car, a a train, ascooter, etc.), a component of a non-motorized vehicle (e.g., a bicycle,a skateboard, etc.), a component of a spacecraft (e.g., a spaceship, asatellite, etc.), a wind turbine, a projectile (e.g., a missile), or anyother physical object that is capable of experiencing drag. Method 500then moves from step 520 to step 530.

At step 530 of method 500, periodic riblets (e.g., submerged periodicriblets of FIG. 1A) are formed on a second portion (e.g., second portion130 of FIG. 1A) of the physical object. The second portion of thephysical object is adjacent to the first portion of the physical object.In certain embodiments, each riblet of the periodic riblets has a samelength. The smooth surface of the first portion of the physical objectmay have a same length as the periodic riblets, as measured in thedirection of the length of the periodic riblets.

Method 500 then moves from step 530 to step 540, where each riblet ofthe periodic riblets of the second portion of the physical object isdepressed below a plane of the smooth surface of the first portion ofthe physical object. The peak of each riblet of the periodic riblets maybe at a same level as the plane of the smooth surface of the firstportion of the physical object. In certain embodiments, a constantdistance is formed between each peak (e.g., peaks 112 of FIG. 1A) ofeach riblet of the periodic riblets such that that the distance betweeneach peak is the same. In certain embodiments, a constant distance isformed between each valley (e.g., valleys 114 of FIG. 1A) of each ribletof the periodic riblets such that that the distance between each valleyis the same. Method 500 then moves from step 540 to step 550.

At step 550, a flow is generated over the periodic riblets of the secondportion of the physical object and over the smooth surface of the firstportion of the physical object. For example, the flow may be generatedby an airplane moving through the air at a predetermined speed. The flowdirection (e.g., flow diction 335 of FIG. 3B) runs parallel to thelength of each riblet of the periodic riblets. Method 500 then movesfrom step 550 to step 560, where method 500 determines whether the flowis a gas or a liquid.

If the flow is a gas (e.g., air), method 500 moves from step 560 to step570, where an aerodynamic drag is generated over the submerged ribletpattern that is less than the total aerodynamic drag (i.e., pressuredrag and viscous drag) produced by generating a flow over a smoothsurface without riblets. As indicated in FIG. 4 above, the aerodynamicdrag generated over the submerged riblet pattern that is less than thetotal aerodynamic drag produced by generating a flow over a protrudingriblet pattern (e.g., protruding riblet pattern 410 of FIG. 4). As such,the submerged riblet pattern reduces drag over aerodynamic surfaces,which may reduce fuel costs and increase range in vehicles (e.g.,aircraft) utilizing the submerged riblet pattern.

If the flow is a liquid (e.g., water), method 500 advances from step 560to step 580, where a hydrodynamic drag is generated over the submergedriblet pattern that is less than the total hydrodynamic drag (i.e.,pressure drag and viscous drag) produced by generating a flow over asmooth surface without riblets. As indicated in FIG. 4 above, thehydrodynamic drag generated over the submerged riblet pattern that isless than the total hydrodynamic drag produced by generating a flow overa protruding riblet pattern (e.g., protruding riblet pattern 410 of FIG.4). As such, the submerged riblet pattern reduces drag over hydrodynamicsurfaces, which may reduce fuel costs and increase range in vehicles(e.g., marine vessels) utilizing the submerged riblet pattern. Method500 then moves from steps 570 and 580 to step 590, where method 500ends.

Modifications, additions, or omissions may be made to method 500depicted in FIG. 5. Method 500 may include more, fewer, or other steps.For example, method 500 may include forming each peak of each riblet ofthe periodic riblets at an angle between 45 degrees and 135 degrees(e.g., 90 degrees.) As another example, method 500 may include formingeach valley between adjacent riblets of the periodic riblets at an anglebetween 45 degrees and 135 degrees (e.g., 90 degrees.) As still anotherexample, method 500 may repeat steps 520 through 540 to form anintermittent pattern along a predetermined length of a component (e.g.,an aircraft wing.)

Steps of method 500 depicted in FIG. 5 may be performed in parallel orin any suitable order. For example, step 520 directed to forming asmooth surface on a first portion of a physical object and step 530directed to forming periodic riblets on a second portion of the physicalobject may be reversed. Any suitable component may perform any step ofmethod 500. For example, one or more machines (e.g., robotic machines)may be used to form one or more surfaces of the physical object.

Embodiments of this disclosure may be applied to any fluid flowapplication where the boundary layer is turbulent and skin friction issignificant. For example, embodiments of this disclosure may be used toreduce internal flow drag in propulsion systems, reduce pipe flow drag,reduce drag in automotive systems, and the like.

Herein, “or” is inclusive and not exclusive, unless expressly indicatedotherwise or indicated otherwise by context. Therefore, herein, “A or B”means “A, B, or both,” unless expressly indicated otherwise or indicatedotherwise by context. Moreover, “and” is both joint and several, unlessexpressly indicated otherwise or indicated otherwise by context.Therefore, herein, “A and B” means “A and B, jointly or severally,”unless expressly indicated otherwise or indicated otherwise by context.

The scope of this disclosure encompasses all changes, substitutions,variations, alterations, and modifications to the example embodimentsdescribed or illustrated herein that a person having ordinary skill inthe art would comprehend. The scope of this disclosure is not limited tothe example embodiments described or illustrated herein. Moreover,although this disclosure describes and illustrates respectiveembodiments herein as including particular components, elements,feature, functions, operations, or steps, any of these embodiments mayinclude any combination or permutation of any of the components,elements, features, functions, operations, or steps described orillustrated anywhere herein that a person having ordinary skill in theart would comprehend. Furthermore, reference in the appended claims toan apparatus or system or a component of an apparatus or system beingadapted to, arranged to, capable of, configured to, enabled to, operableto, or operative to perform a particular function encompasses thatapparatus, system, component, whether or not it or that particularfunction is activated, turned on, or unlocked, as long as thatapparatus, system, or component is so adapted, arranged, capable,configured, enabled, operable, or operative. Additionally, although thisdisclosure describes or illustrates particular embodiments as providingparticular advantages, particular embodiments may provide none, some, orall of these advantages.

What is claimed is:
 1. A method for reducing drag, comprising: forming asmooth surface on a first portion of a physical object; forming periodicriblets on a second portion of the physical object, wherein: the secondportion of the physical object is adjacent to the first portion of thephysical object; and each riblet of the periodic riblets of the secondportion of the physical object is depressed below a plane of the smoothsurface of the first portion of the physical object; and generating aflow over the periodic riblets of the second portion of the physicalobject and over the smooth surface of the first portion of the physicalobject, wherein a length of each riblet of the periodic riblets runsparallel to a direction of the flow.
 2. The method of claim 1, whereinthe physical object is associated with one of the following: anaircraft; a marine vessel; a vehicle; a pipeline; a wind turbine; and aprojectile.
 3. The method of claim 1, further comprising: forming aconstant distance between each peak of each riblet of the periodicriblets; forming each peak of each riblet of the periodic riblets at a90 degree angle; and forming each valley between adjacent riblets of theperiodic riblets at a 90 degree angle.
 4. The method of claim 1, furthercomprising forming each peak of each riblet of the periodic riblets at asame level as the plane of the smooth surface of the first portion ofthe physical object.
 5. The method of claim 1, further comprising:forming each riblet of the periodic riblets at a same length; andforming the smooth surface of the first portion of the physical objectat the same length as the periodic riblets.
 6. The method of claim 1,wherein: a maximum height of each riblet of the periodic riblets is lessthan 0.002 inches; a maximum width of each riblet of the periodicriblets is less than 0.004 inches; and a length of each riblet of theperiodic riblets is within a range of 10 to 50 times longer than themaximum height of each respective riblet.
 7. The method of claim 1,wherein: the first portion of the physical object further comprises atransition surface; an angle between the transition surface of the firstportion of the physical object and the smooth surface of the firstportion of the physical object is within a range of 90 degrees to 179degrees; and each riblet of the periodic riblets terminates at thetransition surface of the first portion of the physical object.
 8. Aphysical object, comprising: a first portion comprising a smoothsurface; and a second portion comprising periodic riblets, wherein: thesecond portion of the physical object is adjacent to the first portionof the physical object; and each riblet of the periodic riblets of thesecond portion of the physical object is depressed below a plane of thesmooth surface of the first portion of the physical object.
 9. Thephysical object of claim 8, wherein the physical object is associatedwith one of the following: an aircraft; a marine vessel; a vehicle; apipeline; a wind turbine; and a projectile.
 10. The physical object ofclaim 8, wherein: a distance between each peak of each riblet of theperiodic riblets is constant; each peak of each riblet of the periodicriblets forms a 90 degree angle; and each valley between adjacentriblets of the periodic riblets forms a 90 degree angle.
 11. Thephysical object of claim 8, wherein each peak of each riblet of theperiodic riblets is at a same level as the plane of the smooth surfaceof the first portion of the physical object.
 12. The physical object ofclaim 8, wherein: each riblet of the periodic riblets has a same length;and the length of the periodic riblets is the same as a length of thesmooth surface of the first portion of the physical object.
 13. Thephysical object of claim 8, wherein: a maximum height of each riblet ofthe periodic riblets is less than 0.002 inches; a maximum width of eachriblet of the periodic riblets is less than 0.004 inches; and a lengthof each riblet of the periodic riblets is within a range of 10 to 50times longer than the maximum height of each respective riblet.
 14. Thephysical object of claim 8, wherein: the first portion of the physicalobject further comprises a transition surface; an angle between thetransition surface of the first portion of the physical object and thesmooth surface of the first portion of the physical object is within arange of 90 degrees to 179 degrees; and each riblet of the periodicriblets terminates at the transition surface of the first portion of thephysical object.
 15. A method of manufacturing a physical object,comprising: forming a smooth surface on a first portion of a physicalobject; and forming periodic riblets on a second portion of the physicalobject, wherein: the second portion of the physical object is adjacentto the first portion of the physical object; and each riblet of theperiodic riblets of the second portion of the physical object isdepressed below a plane of the smooth surface of the first portion ofthe physical object.
 16. The method of claim 15, wherein the physicalobject is associated with one of the following: an aircraft; a marinevessel; a vehicle; a pipeline; a wind turbine; and a projectile.
 17. Themethod of claim 15, further comprising: forming a constant distancebetween each peak of each riblet of the periodic riblets; forming eachpeak of each riblet of the periodic riblets at a 90 degree angle; andforming each valley between adjacent riblets of the periodic riblets ata 90 degree angle.
 18. The method of claim 15, further comprisingforming each peak of each riblet of the periodic riblets at a same levelas the plane of the smooth surface of the first portion of the physicalobject.
 19. The method of claim 15, further comprising: forming eachriblet of the periodic riblets at a same length; and forming the smoothsurface of the first portion of the physical object at the same lengthas the periodic riblets.
 20. The method of claim 15, wherein: a maximumheight of each riblet of the periodic riblets is less than 0.002 inches;a maximum width of each riblet of the periodic riblets is less than0.004 inches; and a length of each riblet of the periodic riblets iswithin a range of 10 to 50 times longer than the maximum height of eachrespective riblet.